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Concept module

Doppler Effect

Watch a moving sound source compress wavefronts ahead and stretch them behind, then see how source motion and observer motion combine to change the heard pitch on one bounded classical bench.

Interactive lab

Keep the stage, graph, and immediate control feedback in one working view.

Time

0.00 s / 3.64 sLivePause to inspect a specific moment, then step or scrub through it.

0.00 s3.64 s

Doppler Effect

A compact pass-by bench keeps one moving sound source, one listener on the chosen side, circular wavefronts, and the heard frequency on the same bounded classical-medium model.

Live setup

Doppler state

f_s: 1.1 Hz
v_wave: 3.2 m/s
v_s: 0.45 m/s
side: ahead
v_o: stationary
lambda_side: 2.5 m
f_obs: 1.28 Hz
pitch: 1.16 x

Front spacing = 2.5 m; rear spacing = 3.32 m.
Current separation = 4.4 m; travel delay = 1.6 s.
Source motion changes medium spacing, while observer motion changes the arrival rate on the chosen side.

Graphs

Switch graph views without breaking the live stage and time link.

Source and observer signals

Compares the emitted oscillation with what the observer receives, so the heard pitch shift stays tied to one live source and one live listener.

time (s): 0 to 3.64normalized signal: -1.1 to 1.1

Source signalObserver signal

Hover or scrub to link the graph back to the stage.time (s) / normalized signal

Controls

Adjust the physical parameters and watch the motion respond.

Source frequency

f_{s}

1.1 Hz

Sets how often the source emits wavefronts.

Source speed

v_{s}

0.45 m/s

Moves the source forward through the medium so the front spacing compresses and the rear spacing stretches.

Observer speed

v_{o}

0 m/s

Positive values move the observer toward the source on the chosen side; negative values move away.

Listen aheadSwitch between the compressed front side and the stretched rear side of the moving source.

More tools

Secondary controls, alternate presets, and less-used toggles stay nearby without crowding the main bench.

Show

More presets

Presets

Predict -> manipulate -> observe

Keep the active prompt next to the controls so each change has an immediate visible consequence.

ComparePrompt 1 of 4

Notice which setup changed the spacing in the medium and which setup only changed the observer's arrival rate. Compare mode makes those two causes stop blending together.

Try this

Clone City pass, then make one setup trail behind and the other move toward the source on the front side.

Equation map

See each variable before you move it.

Select a symbol to highlight the matching control and the graph or overlay it most directly changes.

f_{s}

Source frequency

1.1 Hz

Sets how often the source emits new crests before any motion changes their spacing or arrival rate.

Graph: Source and observer signalsGraph: Observer motion and heard frequencyOverlay: Arrival timing

Equations in play

Choose an equation to sync the active symbol, control highlight, and related graph mapping.

More tools

Detailed noticing prompts, guided overlays, and challenge tasks stay available without taking over the main bench.

Hide

What to notice

Use one cause at a time. The strongest prompt should point at a spacing or timing change already visible on the live pass-by bench.

ComparePrompt 1 of 4

Notice which setup changed the spacing in the medium and which setup only changed the observer's arrival rate. Compare mode makes those two causes stop blending together.

Try this

Clone City pass, then make one setup trail behind and the other move toward the source on the front side.

Why it matters

The compare surface shows that two different motion stories can produce different pitch shifts on the same classical bench.

Control: Source speedControl: Observer speedControl: Listen aheadGraph: Source speed and wavefront spacingGraph: Observer motion and heard frequencyOverlay: Front and rear spacingOverlay: Arrival timing

Guided overlays

Focus one overlay at a time to see what it represents and what to notice in the live motion.

3 visible

Overlay focus

Motion vectors

Marks the source and observer motion directions on the same pass-by bench.

What to notice

Source motion and observer motion play different roles in the Doppler story even though both affect the heard pitch.

Why it matters

It prevents spacing changes in the medium from being confused with changes in how fast the observer meets the same wavefronts.

Control: Source speedControl: Observer speedControl: Listen aheadGraph: Observer motion and heard frequencyEquation

v_{s}

Equation

v_{o}

Challenge mode

Use the same pass-by bench to separate spacing changes in the medium from arrival-rate changes at the observer.

0/2 solved

TargetCore

2 of 6 checks

Higher pitch ahead

Keep the emitted tone near 1.1 Hz and tune the live setup so the observer clearly hears a higher pitch on the moving-source bench.

Graph-linkedGuided start2 hints

Suggested start

Start from City pass and keep the same classical medium.

Pending

Open the observer-response graph.

Source and observer signals

Matched

Keep the front-and-rear spacing overlay on.

Matched

Keep the source frequency near the target tone.

1.1

Pending

Keep the source moving clearly forward.

0.45

Pending

Use the compressed chosen-side spacing.

2.5 m

Pending

Raise the observed frequency above the emitted tone.

1.28 Hz

The checklist updates from the live simulation state, active graph, overlays, inspect time, and compare setup.

At t = 0 s, the source emits 1.1 Hz while moving at 0.45 m/s, so the front spacing is 2.5 m and the rear spacing is 3.32 m. The observer on the ahead side is momentarily stationary relative to the medium, receives 1.28 Hz, and hears a higher pitch cue in this bounded classical sound model.

Equation detailsDeeper interpretation, notes, and worked variable context.

Rest wavelength

If the source is not moving through the medium, this is the crest spacing launched each cycle.

λ_{0} = \frac{v _{w a v e}}{f _{s}}

f_{s}

Source frequency 1.1 Hz

Spacing ahead of the moving source

Ahead of the source, each new crest starts from a later, farther-forward position, so the spacing shrinks.

λ_{ah e a d} = \frac{v _{w a v e} - v _{s}}{f _{s}}

f_{s}

Source frequency 1.1 Hz

v_{s}

Source speed 0.45 m/s

Spacing behind the moving source

Behind the source, each new crest starts farther from the older ones, so the spacing stretches.

λ_{b e hin d} = \frac{v _{w a v e} + v _{s}}{f _{s}}

f_{s}

Source frequency 1.1 Hz

v_{s}

Source speed 0.45 m/s

Observed frequency in one medium

Positive $v_o$ means the observer moves toward the source on the chosen side, and $d = +1$ for listening ahead while $d = -1$ for listening behind.

f_{o b s} = f_{s} \frac{v _{w a v e} + v _{o}}{v _{w a v e} - d v _{s}}

This page uses a bounded classical sound model with source speed below wave speed and no shock-wave or relativity effects.

f_{s}

Source frequency 1.1 Hz

v_{s}

Source speed 0.45 m/s

v_{o}

Observer speed 0 m/s

Progress

Not startedMastery: NewLocal-first

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Let the live model runChange one real controlOpen What to notice

Try this setup

Copy the live bench state and reopen this concept with the same controls, graph, overlays, and compare context.

Stable links

Starter track

Step 6 of 90 / 9 complete

Waves

Earlier steps still set up Doppler Effect.

1. Simple Harmonic Motion2. Wave Speed and Wavelength3. Sound Waves and Longitudinal Motion4. Pitch, Frequency, and Loudness / Intensity+5 more steps

Previous step: Beats.

Start from track beginning

Starter track

Step 4 of 50 / 5 complete

Sound and Acoustics

Earlier steps still set up Doppler Effect.

1. Sound Waves and Longitudinal Motion2. Pitch, Frequency, and Loudness / Intensity3. Beats4. Doppler Effect+1 more steps

Previous step: Beats.

Start from track beginning

Short explanation

What the system is doing

The Doppler effect is not about the source changing how often it emits. It is about the observer meeting wavefronts at a different rate when source motion or observer motion changes the spacing and arrival timing along the listening path.

This bounded bench keeps one classical sound medium, one source moving forward, and one observer who can listen ahead or behind while moving toward or away on that chosen side. Wavefront circles, spacing guides, and the heard-frequency trace all come from that same model, so compressed front spacing and stretched rear spacing stay physically connected to the pitch cue.

Key ideas

01A moving source packs wavefronts closer together ahead of itself and spreads them farther apart behind itself.

02Observer motion changes how quickly wavefronts arrive, but it does not rewrite the spacing already set in the medium.

03In this classical sound model, a higher heard pitch means crests are arriving more often, not that the source changed its emitted frequency.

Live Doppler checks

Solve the exact state on screen.

These checks read the same moving-source bench the stage and graphs use, so the formulas stay attached to one honest pass-by scene.

Live valuesFollowing current parameters

For the current source with $v_{w a v e} = 3.2 m/s$ , $f_{s} = 1.1 Hz$ , and $v_{s} = 0.45 m/s$ , what are the front and rear wavefront spacings?

v_{w a v e}

Wave speed

3.2 m/s

f_{s}

Source frequency

1.1 Hz

v_{s}

Source speed

0.45 m/s

λ_{ah e a d}

Front spacing

2.5 m

λ_{b e hin d}

Rear spacing

3.32 m

1. Use the moving-source spacing relations

Use

λ_{ah e a d} = \frac{v _{w a v e} - v _{s}}{f _{s}}

and

λ_{b e hin d} = \frac{v _{w a v e} + v _{s}}{f _{s}}

2. Substitute the live source values

λ_{ah e a d} = \frac{3.2 - 0.45}{1.1} = 2.5 m

and

λ_{b e hin d} = \frac{3.2 + 0.45}{1.1} = 3.32 m

3. Interpret the spacing split

The source is launching each later crest from a farther-forward position, so the front spacing becomes 2.5 m while the rear spacing stretches to 3.32 m.

Current spacing split

λ_{ah e a d} = 2.5 m, λ_{b e hin d} = 3.32 m

Listening ahead means the front spacing is compressed because the source launches each new crest into less remaining space than the rest spacing.

Passing-source checkpoint

You want the same siren to sound lower without changing the emitted frequency. Where should you listen?

Prediction prompt

Choose between staying ahead of the moving source or listening behind it.

Check your reasoning

Listen behind the source.

Behind the source, the wavefront spacing is stretched rather than compressed. That larger spacing means a lower arrival rate and therefore a lower heard pitch in this bounded classical model.

Common misconception

The source must actually emit a higher frequency when it moves toward you.

The emitted frequency stays fixed here. What changes is the spacing and arrival timing along the observer's path.

Source motion changes the front and rear spacing in the medium. Observer motion changes how quickly those already-existing wavefronts are encountered.

Quick test

Variable effect

Question 1 of 3

Use the moving-source bench, not memory alone. These checks separate spacing changes in the medium from arrival-rate changes at the observer.

The source settings stay fixed, but the observer moves toward the source on the chosen side. Which statement is correct?

Choose one answer to reveal feedback, then test the idea in the live system if a guided example is available.

Accessible description

The simulation shows one sound source moving forward through a horizontal medium and one observer on either the front or rear side. Expanding circular wavefronts, front and rear spacing markers, and arrival-timing labels all stay on the same bench.

Changing source speed compresses the front spacing and stretches the rear spacing. Changing observer speed moves the arrival-rate cue without changing the spacing already laid down in the medium.

Graph summary

The first graph compares the emitted source signal with the observer signal over time. The second graph sweeps source speed to show front and rear spacing, and the third graph sweeps observer speed to show the heard frequency against the emitted frequency baseline.

Keep the sound story moving

Keep moving through the concept map.

These suggestions come from the concept registry, so the reason label reflects either curated guidance or the fallback progression logic.

Combine sound sourcesOscillations

Doppler Effect

See each variable before you move it.

Motion vectors

Higher pitch ahead

Waves

Sound and Acoustics

What the system is doing

Solve the exact state on screen.

For the current source with $v_{w a v e} = 3.2 m/s$ , $f_{s} = 1.1 Hz$ , and $v_{s} = 0.45 m/s$ , what are the front and rear wavefront spacings?

The source settings stay fixed, but the observer moves toward the source on the chosen side. Which statement is correct?

Keep moving through the concept map.

Wave Interference

Standing Waves

Sound Waves and Longitudinal Motion

Doppler Effect

See each variable before you move it.

Motion vectors

Higher pitch ahead

Waves

Sound and Acoustics

What the system is doing

Solve the exact state on screen.

For the current source with vwave​=3.2m/s, fs​=1.1Hz, and vs​=0.45m/s, what are the front and rear wavefront spacings?

The source settings stay fixed, but the observer moves toward the source on the chosen side. Which statement is correct?

Keep moving through the concept map.

Wave Interference

Standing Waves

Sound Waves and Longitudinal Motion

For the current source with $v_{w a v e} = 3.2 m/s$ , $f_{s} = 1.1 Hz$ , and $v_{s} = 0.45 m/s$ , what are the front and rear wavefront spacings?